1. Field of the Invention
The present invention relates to a method for controlling a vehicle suspension system, and to an apparatus suitable for actuating the method. In particular, the invention concerns a method and a related apparatus for controlling the damping force characteristic of shock absorbers in a semi-active vehicle suspension system, based on the Sky Hook control theory.
2. Description of the Related Art
The suspension system of a vehicle is intended to perform several functions, such as sustaining the vehicle over the road or, more generally, the ground, keeping the vibrations transmitted to the vehicle body (for example, in the case of a car, the passenger compartment or car body) as low as possible, distributing the forces arising from accelerations, due for example to an increase or a decrease in the vehicle speed and/or to changes in the vehicle ride direction.
Several types of suspension systems have been proposed, which can be grouped in three main categories: passive suspension systems, active suspension systems and semi-active suspension systems.
In passive suspension systems, the shock absorbers have a fixed damping coefficient. In active suspension systems, the shock absorbers have a variable damping coefficient, which can be varied continuously under the control of a control system, for example by means of suitably controlled hydraulic pumps. Active suspension systems can thus perform the above-mentioned functions adapting to the particular ride conditions.
In semi-active suspension systems, similarly to active suspension systems, the damping coefficient of the shock absorbers can be varied continuously under the control of a control system, so as to adapt to the particular ride conditions. However, while in active suspension systems it can be necessary to supply external energy to the shock absorbers to control the damping force characteristic thereof, this is not so in semi-active suspension systems, wherein the control is only directed to properly dissipating the energy of the shock absorbers.
Semi-active suspension systems represent an intermediate solution between passive and active suspension systems, providing better performance than the former without being so expensive as the latter.
The behavior of a passive suspension system including one suspension can be determined using for example the De Carbon model. Such a model, depicted in FIG. 1, is a system with two degrees of freedom, and is for example suitable to represent one fourth (that is, one wheel) of a four-wheels vehicle such as a car. The model system includes a suspended mass 1, of mass M, representing the mass of the car body, and a non-suspended mass 2, of mass m, representing the mass of the wheel. Neglecting the damping effect of the tire, the non-suspended mass m is coupled to ground (the road surface r) by a spring 3 of rigidity kp, corresponding to the tire rigidity. The suspended mass 1 is coupled to the non-suspended mass 2 by means of the suspension, which comprises a spring 4 of rigidity k and a shock absorber 5 having a constant damping coefficient Crel.
Applying the D'Alembert principle to the model system of FIG. 1, the following mathematical model of the suspension can be derived:M·{umlaut over (z)}b=−k·(zb−zw)−Crel·(żb−żw)m·{umlaut over (z)}w=k·(zb−zw)−kp·(zw−h)+Crel·(żb−żw)where zb is vertical coordinate of the suspended mass 1 (the car body) with respect to an arbitrary reference level, zw is the vertical coordinate of the non-suspended mass 1 (the wheel) and h is the height of the road surface r with respect to said reference level. The second time derivative of zb, i.e., the vertical acceleration of the car body, can be adopted as an index of ride comfort assured by the suspension: the lower the vertical acceleration of the car body, the higher the ride comfort. The force exerted by the non-suspended mass 2 (the wheel) onto the road surface r can be adopted as an index of roadholding: the higher the force exerted by the wheel onto the road surface, the higher the car holding of the road. Alternatively, the variation in time of the force exerted by the wheel onto the road during the vehicle ride can be adopted as an index of roadholding.
The limitations of the passive suspension system stems from the fact that only one parameter, i.e., the damping coefficient Crel of the shock absorber, is available for adjusting the two indexes of comfort and roadholding. Since the two requirements are independent from each other, and since the minima of the two indexes are achieved for different values of the shock absorber damping coefficient Crel, the system does not have an optimum solution, and merely a trade-off solution can be found.
In principle, this problem can be solved by increasing the number of system parameters, that is, making the shock absorber damping force to depend on more than a single parameter. One way to do so is represented by the Sky Hook approach.
In a suspension system based on the Sky Hook approach the force exerted by the shock absorber onto the car body is proportional to the absolute speed of the car body with respect to an inertial reference system, and to the relative speed between the car body and the wheel.
Still in principle, as the inertial reference system either the earth or the sky can be taken. However, since the suspended mass cannot be connected to the earth, the sky is chosen as the inertial reference system and the suspended mass is ideally assumed to be hooked to the sky. The corresponding system model is depicted in FIG. 2, where s indicates the sky inertial reference system and 6 denotes a shock absorber of damping coefficient Csky connecting the suspended mass 1 to the sky s.
A Sky Hook damper is merely an ideal device, since it is clearly not possible to couple the suspended mass 1 to the sky. In the practice, a Sky Hook suspension can be implemented by replacing the shock absorber 5, having a fixed damping coefficient Crel, with a shock absorber 50 having a variable damping coefficient, and providing a feedback control from the car body 1 to the shock absorber 50, thus obtaining the model depicted in FIG. 3.
Applying again the D'Alembert principle to the system depicted in FIG. 3, the resulting mathematical is the following:M·{umlaut over (z)}b=−k·(zb−zw)−Famm·{umlaut over (z)}w=k·(zb−zw)−kp·(zw−h)+Famwhere Fam is the force exerted by the shock absorber 50 on the car body 1. The force Fam which, as previously mentioned, must be proportional to the absolute speed of the car body 1 with respect to an inertial reference system and to the relative speed between the car body 1 and the wheel 2 is given by:Fam(t)=Crel(t)·Vrel(t)+Csky(t)·Vabs(t)=Crel·(żb−żw)+Csky·żbhaving indicated as Vrel the relative vertical speed between the car body 1 and the wheel 2, and as Vabs the absolute vertical speed of the car body 1. The time dependence of the damping coefficients Crel and Csky has also been explicitly shown.
It follows that two parameters are now available for controlling the suspension, that are the damping coefficients Crel and Csky.
The Sky-Hook control technique can be implemented both in active and in semi-active suspension systems. Since, as mentioned before, in a semi-active suspension system, differently from active suspensions systems, no external energy is supplied to the suspension system but rather the energy of the suspension system itself is dissipated in a controlled way, in a semi-active suspension system the shock absorber 50 applies no force to the car body 1 when such a force should be opposite to the relative speed of the car body 1 with respect to the wheel 2.
Consequently, while in both the active and semi-active suspension systems is:Fam=Crel·(żb−żw)+Csky·żb for Fam·(żb−żw)>0the semi-active suspension system has the following additional limitation:Fam=0 for Fam·(żb−żw)<0
Conventional Sky Hook suspension control methods provide for choosing the pair of parameters Crel and Csky in such a way as to find a trade-off between the contrasting requirements of minimizing the car body vertical acceleration, so as to maximize the comfort index, and minimizing the variation of the force exerted by the wheel on the road surface, so as to maximize the index of roadholding.
A weight factor p is determined which is used to weight the two contributes; by introducing the weight factor p, the function to be minimized becomes:Fopt=p·(M·{umlaut over (z)}b)+(1−p)·Fgndwhere by Fgnd the variation of the force exerted by the wheel onto the road is indicated.
Once a value for the weight factor p has been chosen, the values for the damping coefficients Crel and Csky can be univocally determined by minimizing (i.e., searching the minimum) the function Fopt. The choice of the value for the weight factor p determines the type of driving style; changing the value of the weight factor p, either the ride comfort or the roadholding can be privileged.
Up to now, in the implementation of the sky Hook control approach in semi-active suspension systems the value of the weight factor p has been fixed a priori, and the values for the damping coefficients Crel and Csky univocally determined on the basis of the value of the weight factor p by using conventional control systems, like P-I-D (Proportional-Integral-Derivative) controllers.